840/1575

Since 840 ends with a 0 and 1575 ends with a 5, they can
both be divided by 5, 840÷5=168 and 1575÷5=315.

So the fraction is now reduced to 168/315

168 has sum of digits 15 and 315 has sum of digits 9, so they are
both divisible by 3, 168÷3=56 and 315÷3=105.

So the fraction is now reduced to 56/105

We know from our multiplication facts that 7×8=56.  105 is not even, so
there's no use to try 8, so let's try to see if 105 is divisible by 7
Yes it is.  56÷7=8 and 105÷7=15.

So the fraction is 8/15, and that cannot be reduced further.

Answer: 8/15

Edwin